{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# §8 Statistics\n",
    "\n",
    "## Content\n",
    "\n",
    "    8.1 probability distribution\n",
    "    8.2 Statistics\n",
    "    8.3 parameter estimation\n",
    "    8.4 hypothesis testing\n",
    "    8.5 linear regression\n",
    "    8.6 analysis of variance\n",
    "    8.7 nonparameteric statistics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8.1 probability distribution\n",
    "\n",
    "### 8.1.1 basic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array(1.), array(4.))\n",
      "(array(1.), array(4.), array(0.), array(0.))\n",
      "1.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import scipy.stats as ss\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "X = ss.norm(loc=1, scale=2) #X is a random variable subject to normal distribution\n",
    "print(X.stats()) #mean and variance\n",
    "print(X.stats(moments='mvsk')) #mean, variance, skewness and kurtosis\n",
    "print(X.ppf(0.5)) #Inverse function of cumulative distribution (quantile)\n",
    "t = np.arange(-4,6,0.001)\n",
    "plt.plot(t, X.pdf(t)) #Probability Density Function\n",
    "plt.plot(t, X.cdf(t)) #Cumulative Distribution Function\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8.1.2 Discrete distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 1 6 2 1 1 2 4 6 1 1 5 1 1 1 2 2 3 3]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = range(1,7)\n",
    "p = (0.4,0.2,0.1,0.1,0.1,0.1)\n",
    "dice = ss.rv_discrete(values=(X,p))\n",
    "print(dice.rvs(size=20))\n",
    "\n",
    "lambda_ = 10.\n",
    "t = np.arange(20)\n",
    "ps = ss.poisson.pmf(t, lambda_) #Probability Density Function\n",
    "bi = ss.binom.pmf(t, 100, lambda_/100)\n",
    "plt.plot(t, ps, label='Poisson distribution')\n",
    "plt.plot(t, bi, label='Binomial distribution')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2 2 2 1 1 1 2 1 1 0 2 2 1 2 2 2 1 1 2 0 1 2 2 1 0 1 1 1 2 0 2 0 1 1 1 2 1\n",
      " 2 0 2 1 2 2 2 1 1 0 1 1 2 2 2 0 1 1 2 2 2 1 2 0 2 2 2 1 2 1 2 2 0 1 2 1 2\n",
      " 0 1 2 2 2 2 1 1 1 1 2 0 2 2 2 1 2 1 2 1 1 2 1 2 2 2]\n"
     ]
    }
   ],
   "source": [
    "b = ss.binom(2, 0.7)\n",
    "print(b.rvs(100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8.1.3 Three main statistical distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import scipy.special as S\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x = np.linspace(0,14,1000)\n",
    "\n",
    "for n in [1,2,4,6,11]:\n",
    "    #y = 1./(2**(n/2.))/S.gamma(n/2.) * (x**(n/2.-1))*np.exp(-x/2)\n",
    "    #plt.plot(x,y,label='n=%d'%n)\n",
    "    p = ss.chi2.pdf(x, n) #n is degree of freedom\n",
    "    plt.plot(x, p, label='n=%d'%n)\n",
    "    \n",
    "plt.legend()\n",
    "plt.title(r'$\\chi^2 \\, distribution$')\n",
    "plt.axis([0,15,0,0.4])\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.spines['top'].set_color('none')\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['bottom'].set_position(('data',0))\n",
    "ax.spines['left'].set_position(('data',0))\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "t distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import scipy.special as S\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x = np.linspace(-5,5,1000)\n",
    "\n",
    "for n in [1,2,10]:\n",
    "    p = ss.t.pdf(x, n) #n is degree of freedom\n",
    "    plt.plot(x, p, label='n=%d'%n)\n",
    "plt.plot(x, ss.norm.pdf(x), ls='--', label='∞')\n",
    "    \n",
    "plt.legend()\n",
    "plt.title('t distribution')\n",
    "plt.axis([-5,5,0,0.4])\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.spines['top'].set_color('none')\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['bottom'].set_position(('data',0))\n",
    "ax.spines['left'].set_position(('data',0))\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "F distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for n,m in [(4,4), (10,4), (10,10), (4,10)]:\n",
    "    plt.plot(x, ss.f.pdf(x,n,m),label='n=%d %d'%(n,m)) #n and m are degree of freedom\n",
    "    \n",
    "plt.legend()\n",
    "plt.title('F distribution')\n",
    "plt.axis([0,4,0,0.8])\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.spines['top'].set_color('none')\n",
    "ax.spines['right'].set_color('none')\n",
    "ax.spines['bottom'].set_position(('data',0))\n",
    "ax.spines['left'].set_position(('data',0))\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8.1.4 other distribution\n",
    "    \n",
    "    geom\n",
    "    hypergeom\n",
    "    zipf\n",
    "    \n",
    "    beta \n",
    "    gamma\n",
    "    lognorm \n",
    "    uniform, paramters of pdf: a,b \n",
    "    cauchy\n",
    "    laplace\n",
    "    rayleigh\n",
    "    expon, paramters of pdf: θ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8.2 Statistics\n",
    "\n",
    "### 8.2.1 statistic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-3.5552385906048176, -3.38614786154655, -2.6730758624963338, -2.562491971249888, -1.819637304666443, -1.7965945850367775, -1.5271879860659698, -1.1215613358634284, -0.9629410206634892, -0.8750242638932231, -0.8456054528195771, -0.7890540652043343, -0.6376062321101648, -0.5490711772463568, -0.3760440892404784, -0.359830287637408, -0.25356754150774785, -0.19117828702665807, -0.16127218550614586, 0.15664948164099424, 0.15755812303257488, 0.20740093968461304, 0.2322816235156645, 0.308245189713548, 0.4553376556410873, 0.5011736681577168, 0.5547123004560292, 0.6824564774613682, 0.7915868806088537, 0.8613579818385468, 1.0240485294127681, 1.0694163436930804, 1.0922211592114741, 1.1892789167555058, 1.8197910184385298, 1.9656547244545712, 2.2010743076273664, 2.214080975932784, 2.2332050215000376, 2.2630982237413244, 2.2743255985167585, 2.4119537378371168, 2.887859013892488, 3.1068773413250925, 3.3046705259462903, 3.3728176469075017, 3.589201273491847, 4.356160642721795, 5.016042068904182, 5.082854732579341]\n",
      "0.6588052404851013 3.983761221253081 1.9959361766482115 0.47825566189940205\n"
     ]
    }
   ],
   "source": [
    "x = X.rvs(size=50) #random value\n",
    "print(sorted(x))\n",
    "print(np.mean(x), np.var(x), np.std(x), np.median(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2, 50)\n",
      "[[ 3.52026193 -0.23938506]\n",
      " [-0.23938506  2.42212483]]\n",
      "[[ 1.         -0.08198064]\n",
      " [-0.08198064  1.        ]]\n"
     ]
    }
   ],
   "source": [
    "x2 = X.rvs(size=50)\n",
    "xx = np.vstack([x,x2])\n",
    "print(xx.shape)\n",
    "print(np.cov(xx)) #covariance\n",
    "print(np.corrcoef(xx)) #correlation coefficient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.10612554603299981 1.3682094560851645\n",
      "3.566776174436166\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "pdx = pd.Series(x)\n",
    "print(pdx.skew(), pdx.kurt())\n",
    "print(pdx.quantile(0.9))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8.2.2 Statistical chart\n",
    "\n",
    "**histogram**\n",
    "\n",
    "matplotlib.pyplot.hist(x, bins=None, range=None, normed=False, weights=None, cumulative=False, bottom=None, histtype='bar', align='mid', orientation='vertical', rwidth=None, log=False, color=None, label=None, stacked=False, hold=None, data=None, **kwargs)\n",
    "\n",
    "https://matplotlib.org/2.0.2/api/pyplot_api.html?highlight=hist#matplotlib.pyplot.hist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.  2.  3. 10. 12. 12.  6.  2.  1.  1.]\n",
      "[-4.69886333 -3.46100233 -2.22314133 -0.98528033  0.25258067  1.49044167\n",
      "  2.72830267  3.96616367  5.20402467  6.44188567  7.67974667]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n, bins, patches = plt.hist(x)\n",
    "print(n)\n",
    "print(bins)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Boxplot**\n",
    "\n",
    "Box plots show the five-number summary of a set of data: including the minimum score, first (lower) quartile, median, third (upper) quartile, and maximum score.\n",
    "\n",
    "matplotlib.pyplot.boxplot(x, notch=None, sym=None, vert=None, whis=None, positions=None, widths=None, patch_artist=None, bootstrap=None, usermedians=None, conf_intervals=None, meanline=None, showmeans=None, showcaps=None, showbox=None, showfliers=None, boxprops=None, labels=None, flierprops=None, medianprops=None, meanprops=None, capprops=None, whiskerprops=None, manage_xticks=True, autorange=False, zorder=None, hold=None, data=None)\n",
    "\n",
    "https://matplotlib.org/2.0.2/api/pyplot_api.html?highlight=boxplot#matplotlib.pyplot.boxplot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2, 50)\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.boxplot(xx.T)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Q-Q plots**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sort_x = sorted(x)\n",
    "n = len(x)\n",
    "xi = (np.arange(1,n+1) - 1/2) / n\n",
    "yi = ss.norm.ppf(xi, np.mean(x), np.std(x))\n",
    "plt.scatter(yi, sort_x, c='b')\n",
    "min_, max_= x.min()-0.2, x.max()+0.2\n",
    "plt.axis([min_, max_, min_, max_])\n",
    "plt.plot([min_,max_], [min_,max_], 'r-')\n",
    "plt.xlabel('Theoretical quantiles')\n",
    "plt.ylabel('Ordered Values')\n",
    "plt.title('Q-Q plots')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "scipy.stats.probplot(x, sparams=(), dist='norm', fit=True, plot=None, rvalue=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ss.probplot(x, plot=plt)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Kernel density estimation**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:4: MatplotlibDeprecationWarning: \n",
      "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n",
      "  after removing the cwd from sys.path.\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kde = ss.gaussian_kde(x)\n",
    "x_eval = np.linspace(min_, max_, 1000)\n",
    "plt.plot(x_eval, kde(x_eval), c='r')\n",
    "plt.hist(x, normed=True)\n",
    "plt.plot(x_eval, X.pdf(x_eval), 'g--')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8.3 parameter estimation \n",
    "\n",
    "### 8.3.1 estimating parameters\n",
    "\n",
    "Suppose X<sub>1</sub>, X<sub>2</sub>, ..., X<sub>n</sub> is a random sample from a pdf f(x) whose unknown paramter is θ, how to extimate it?\n",
    "\n",
    "maximum likelihood estimation\n",
    "\n",
    "fit can only use for continuous distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0.6588052404851013, 1.9959361766482115)\n"
     ]
    }
   ],
   "source": [
    "print(ss.norm.fit(x)) #fit a normal distribution from samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.705\n"
     ]
    }
   ],
   "source": [
    "b = ss.binom(2, 0.7)\n",
    "sample = b.rvs(100)\n",
    "print(np.sum(sample)/100/2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8.3.2 interval estimation\n",
    "\n",
    "The usual way to quantify the amount of uncertainty in an estimator is to construct a confidence interval.\n",
    "\n",
    "e.g. A batch of candy whose weight obey normal distribution. Now select 16 bags randomly. Their weights are given. Find the confidence interval of mean with confidence level 0.95"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "503.75\n",
      "confidence interval is (500.44510746243924, 507.05489253756076)\n"
     ]
    }
   ],
   "source": [
    "a = np.array([506,508,499,503,504,510,497,512,514,505,493,496,506,502,509,496])\n",
    "print(a.mean())\n",
    "alpha = 0.95\n",
    "df = len(a)-1\n",
    "ci = ss.t.interval(alpha, df, loc=a.mean(), scale=ss.sem(a))\n",
    "print('confidence interval is', ci)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8.4 hypothesis testing\n",
    "\n",
    "The P-value associated with an observed test statistic is the probability of getting a value for that test statistic as extreme as or more extreme than what was actually observed (relative to H<sub>1</sub>) given that H<sub>0</sub> is true. If the P-value is less than or equal to α, the null hypothesis can be rejected at the α level of significance. Or, the P-value is the smallest α at which we can reject H<sub>0</sub>. \n",
    "\n",
    "statsmodels.stats.weightstats.ztest(x1, x2=None, value=0, alternative='two-sided', usevar='pooled', ddof=1.0)\n",
    "\n",
    "https://www.statsmodels.org/stable/generated/statsmodels.stats.weightstats.ztest.html#statsmodels.stats.weightstats.ztest"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### μ testing with σ<sup>2</sup> known (One-sample Z test)\n",
    "\n",
    "$H_0:\\mu=\\mu_0, H_1:\\mu\\neq\\mu_0$\n",
    "\n",
    "$Z=\\frac{\\overline{X}-\\mu_0}{\\sigma/\\sqrt{n}}$\n",
    "\n",
    "e.g. A workshop uses a packaging machine to package candy. The weight of bagged candy is a random variable, which follows a normal distribution. When the machine is normal, its mean value is 0.5kg, and the standard deviation is 0.015kg. In order to check whether the packaging machine is normal after the commencement of work on a certain day, randomly take 9 bags of sugar packed by it, weigh the net weight as 0.497,0.506,0.518,0.524,0.498,0.511,0.520,0.515,0.512. At the significance level α=0.05, ask whether the machine is normal?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "z value is: 2.2444\n",
      "3.584920298041139 0.0003371811598441\n"
     ]
    }
   ],
   "source": [
    "from statsmodels.stats.weightstats import ztest\n",
    "\n",
    "sigma=0.015\n",
    "a = np.array([0.497,0.506,0.518,0.524,0.498,0.511,0.520,0.515,0.512])\n",
    "tstat1, pvalue = ztest(a, value=0.5)\n",
    "tstat2 = tstat1 * a.std(ddof=1) / sigma\n",
    "print('z value is:', round(tstat2, 4))\n",
    "print(tstat1, pvalue)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "p-value < 0.05, reject H<sub>0</sub>, that is the packaging machine is abnormal \n",
    "___"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### μ testing with σ<sup>2</sup> unknown (One-sample t test)\n",
    "\n",
    "$H_0:\\mu=\\mu_0, H_1:\\mu\\neq\\mu_0$\n",
    "\n",
    "$T=\\frac{\\overline{X}-\\mu_0}{S/\\sqrt{n}}$\n",
    "\n",
    "e.g. The nickel content in five samples of a batch of ore sands is determined to be 3.25, 3.27, 3.24, 3.26, 3.24 (%). Suppose that the measured value generally follows normal distribution, but the parameters are unknown. Can you accept the assumption that the average nickel content of this batch of ore sands is 3.25 under α=0.01?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.34299717028498317 0.7316005889599273\n"
     ]
    }
   ],
   "source": [
    "a = np.array([3.25, 3.27, 3.24, 3.26, 3.24])\n",
    "tstat1, pvalue = ztest(a, value=3.25)\n",
    "print(tstat1, pvalue)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "p-value > 0.01, accept H<sub>0</sub>. The average is 3.25.\n",
    "___"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$H_0:\\mu\\geq\\mu_0, H_1:\\mu<\\mu_0$\n",
    "\n",
    "e.g. According to the regulations, the average vitamin C content in 100g canned tomato juice shall not be less than 21 mg/g. Now, 17 cans are taken from the products of the factory, and the vitamin C content measured in 100g tomato juice is 16,25,21,20,23,21,19,15,13,23,17,20,29,18,22,16,22. Assuming that the vitamin content follows the normal distribution, and the parameters are unknown, whether these cans meet the requirements (take the significance level α=0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1.0348266239966402 0.15037494342517732\n"
     ]
    }
   ],
   "source": [
    "a = np.array([16,25,21,20,23,21,19,15,13,23,17,20,29,18,22,16,22])\n",
    "tstat1, pvalue = ztest(a, value=21, alternative='smaller')\n",
    "print(tstat1, pvalue)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "p-value > 0.05, accpet H<sub>0</sub>, that is the cans meet the requirements \n",
    "___"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### μ testing (Two-sample t test)\n",
    "\n",
    "$H_0:\\mu_1=\\mu_2, H_1:\\mu_1\\neq\\mu_2$\n",
    "\n",
    "$T=\\frac{\\overline{X}-\\overline{X}}{\\sqrt{\\frac{(n_1-1)S_1^{2}+(n_2-1)S_2^{2}}{n_1+n_2-1}} \\cdot \\sqrt{\\frac{1}{n_1}+\\frac{1}{n_2}}}$\n",
    "\n",
    "e.g. The proportion of three letter words in Mark Twain's eight novels is 0.225,0.262,0.217,0.240,0.230,0.229,0.235,0.217, while the proportion of Snodgrass's 10 novels is 0.209,0.205,0.196,0.210,0.202,0.207,0.224,0.223,0.220,0.201.\n",
    "Suppose that the two groups of data are from normal populations, and the variance of the two populations is equal, but the parameters are unknown, and the two samples are independent of each other. Ask the two writers whether there is a significant difference in the proportion of three letter words in their novels (take the significance level α=0.05)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.8781376258607807 0.00010525916870096611\n"
     ]
    }
   ],
   "source": [
    "a = np.array([0.225,0.262,0.217,0.240,0.230,0.229,0.235,0.217])\n",
    "b = np.array([0.209,0.205,0.196,0.210,0.202,0.207,0.224,0.223,0.220,0.201])\n",
    "tstat1, pvalue = ztest(a, b, value=0)\n",
    "print(tstat1, pvalue)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### correlation\n",
    "\n",
    "The Pearson correlation coefficient measures the linear relationship between two datasets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(-0.02888047643799556, 0.8421907340088544)\n"
     ]
    }
   ],
   "source": [
    "print(ss.pearsonr(x, x2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "p-value = 0.842 > 0.05, so x and x2 has no linear relationship"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8.5 linear regression\n",
    "\n",
    "$y = \\beta_{0}+\\beta_{1}x+\\epsilon$\n",
    "\n",
    "$min \\, Q=\\sum_{i=1}^n (y_{i}-\\beta_{0}-\\beta_{1}x_{i})^2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-23.950588628514122 266.166255059977\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                  Heart   R-squared:                       0.721\n",
      "Model:                            OLS   Adj. R-squared:                  0.705\n",
      "Method:                 Least Squares   F-statistic:                     43.99\n",
      "Date:                Tue, 08 Nov 2022   Prob (F-statistic):           4.23e-06\n",
      "Time:                        16:48:52   Log-Likelihood:                -95.241\n",
      "No. Observations:                  19   AIC:                             194.5\n",
      "Df Residuals:                      17   BIC:                             196.4\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept    266.1663     14.044     18.953      0.000     236.537     295.796\n",
      "Alcohol      -23.9506      3.611     -6.633      0.000     -31.569     -16.332\n",
      "==============================================================================\n",
      "Omnibus:                        2.827   Durbin-Watson:                   2.120\n",
      "Prob(Omnibus):                  0.243   Jarque-Bera (JB):                1.192\n",
      "Skew:                          -0.076   Prob(JB):                        0.551\n",
      "Kurtosis:                       1.783   Cond. No.                         6.45\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\stats\\stats.py:1450: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=19\n",
      "  \"anyway, n=%i\" % int(n))\n"
     ]
    }
   ],
   "source": [
    "import statsmodels.formula.api as smf\n",
    "import pandas as pd\n",
    "\n",
    "x = np.array([2.5,3.9,2.9,2.4,2.9,0.8,9.1,0.8,0.7,7.9,1.8,1.9,0.8,6.5,1.6,5.8,1.3,1.2,2.7])\n",
    "y = np.array([211,167,131,191,220,297,71,211,300,107,167,266,277,86,207,115,285,199,172])\n",
    "\n",
    "plt.plot(x,y,'+k', label='data points')\n",
    "p = np.polyfit(x,y,deg=1)\n",
    "print(p[0], p[1])\n",
    "plt.plot(x, np.polyval(p,x), label='fit line')\n",
    "plt.xlabel('Alcohol consumption')\n",
    "plt.ylabel('Heart disease mortality')\n",
    "plt.show()\n",
    "\n",
    "data = pd.DataFrame({'Alcohol':x, 'Heart':y})\n",
    "model = smf.ols(formula='Heart ~ Alcohol', data=data).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intercept    266.166255\n",
      "Alcohol      -23.950589\n",
      "dtype: float64\n",
      "0    206.289783\n",
      "1    172.758959\n",
      "2    196.709548\n",
      "3    208.684842\n",
      "4    196.709548\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(model.params)\n",
    "print(model.predict(data['Alcohol'][:5]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Explain of summary:\n",
    "    \n",
    "No. Observations: size of sample x\n",
    "\n",
    "Df Residuals：degree of freedom of residuals，= No.Observations - Df Model - 1\n",
    "\n",
    "Df Model：degree of freedom of model，=dim X\n",
    "\n",
    "R-squared：=SSR/SST，range is [0, 1]，close to 1 means the regression effect is good\n",
    "\n",
    "F-statistic：H<sub>0</sub> is model is not a linear model. We will reject the H<sub>0</sub> if F-statistic is large.\n",
    "\n",
    "Omnibus：Test of data normality based on kurtosis and skewness.\n",
    "\n",
    "Durbin-Watson: Check whether there is autocorrelation in the residuals. It mainly tests whether there is autocorrelation in the regression residuals by determining whether the correlation of two adjacent error items is zero.\n",
    "\n",
    "___\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "alternative method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                 Results: Ordinary least squares\n",
      "=================================================================\n",
      "Model:              OLS              Adj. R-squared:     0.705   \n",
      "Dependent Variable: y                AIC:                194.4811\n",
      "Date:               2022-11-08 17:01 BIC:                196.3700\n",
      "No. Observations:   19               Log-Likelihood:     -95.241 \n",
      "Df Model:           1                F-statistic:        43.99   \n",
      "Df Residuals:       17               Prob (F-statistic): 4.23e-06\n",
      "R-squared:          0.721            Scale:              1478.3  \n",
      "------------------------------------------------------------------\n",
      "            Coef.    Std.Err.     t     P>|t|    [0.025    0.975] \n",
      "------------------------------------------------------------------\n",
      "const      266.1663   14.0437  18.9527  0.0000  236.5365  295.7960\n",
      "x1         -23.9506    3.6110  -6.6327  0.0000  -31.5691  -16.3321\n",
      "-----------------------------------------------------------------\n",
      "Omnibus:               2.827        Durbin-Watson:          2.120\n",
      "Prob(Omnibus):         0.243        Jarque-Bera (JB):       1.192\n",
      "Skew:                  -0.076       Prob(JB):               0.551\n",
      "Kurtosis:              1.783        Condition No.:          6    \n",
      "=================================================================\n",
      "\n",
      "[266.16625506 -23.95058863]\n",
      "[74.56154603]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\stats\\stats.py:1450: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=19\n",
      "  \"anyway, n=%i\" % int(n))\n"
     ]
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "\n",
    "#Add a constant 1, \n",
    "#which corresponds to the intercept of the regression line on the y-axis\n",
    "X = sm.add_constant(x)\n",
    "#Modeling with Least Squares\n",
    "md = sm.OLS(y,X).fit()\n",
    "\n",
    "print(md.summary2())\n",
    "print(md.params)\n",
    "print(md.predict([1,8])) #the first element must be 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8.6 analysis of variance\n",
    "\n",
    "### 8.6.1 Single factor analysis\n",
    "\n",
    "In a test, if only one factor A is considered and other factors remain unchanged, it is called a single factor test. The specific method is: A take several (r) levels and conduct several tests at each level. Our task is to infer from the test results whether factor A has a significant impact on the indicators, which is equivalent to testing whether the mean values of several populations are equal.\n",
    "\n",
    "The t-test can be used to test whether the mean values of any two adjacent populations are equal. However, it is necessary to check r-1 times.\n",
    "\n",
    "The null hypothesis of variance analysis is $H_0: \\mu_0=\\mu_1=\\cdots=\\mu_r$\n",
    "\n",
    "e.g. In order to check whether the labor productivity of five workers is the same, the output of four days per person is recorded, as shown below\n",
    "\n",
    "    256,254,250,248,236\n",
    "    242,330,277,280,252\n",
    "    280,290,230,305,220\n",
    "    298,295,302,289,252\n",
    "Can we infer from these data whether there is a significant difference in their productivity?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            df   sum_sq   mean_sq         F    PR(>F)\n",
      "C(x)       4.0   6125.7  1531.425  2.261741  0.110913\n",
      "Residual  15.0  10156.5   677.100       NaN       NaN\n"
     ]
    }
   ],
   "source": [
    "a = np.array([[256,254,250,248,236],\n",
    "              [242,330,277,280,252],\n",
    "              [280,290,230,305,220],\n",
    "              [298,295,302,289,252]])\n",
    "x = np.arange(1,6).repeat(4)\n",
    "d = {'x':x, 'y':a.T.flatten()}\n",
    "model = smf.ols('y~C(x)', d).fit()\n",
    "anovat = sm.stats.anova_lm(model)\n",
    "print(anovat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PR = 0.110913 > 0.05, so there is no significant difference in the productivity of five workers."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8.6.2 Multi factor analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "TODO\n",
    "\n",
    "https://www.bbsmax.com/A/amd0NN41Jg/\n",
    "\n",
    "https://blog.csdn.net/Kaitiren/article/details/85066793"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8.7 nonparameteric statistics\n",
    "\n",
    "the Kolmogorov-Smirnov test\n",
    "\n",
    "p-value > 0.05 is yes, suite for small sample\n",
    "\n",
    "e.g. 50 balls were randomly selected from the production of balls in a workshop, and their diameters (mm) were measured to be \n",
    "\n",
    "    15.0,15.5,15.2,15.1,15.9,14.7,14.8,15.5,15.6,15.3,\n",
    "    15.1,15.3,15.0,15.6,15.7,14.8,14.5,14.2,14.9,14.9,\n",
    "    15.2,15.0,15.3,15.6,15.1,14.9,14.2,14.6,15.8,15.2,\n",
    "    15.9,15.2,15.0,14.9,14.8,14.5,15.1,15.5,15.5,15.1,\n",
    "    15.1,15.0,15.3,14.7,14.5,15.5,15.0,14.7,14.6,14.2\n",
    "Ask if the ball diameters conform to the normal distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.08345510804577916 0.8770924349305106\n"
     ]
    }
   ],
   "source": [
    "import scipy.stats as ss\n",
    "\n",
    "a = np.array([15.0,15.5,15.2,15.1,15.9,14.7,14.8,15.5,15.6,15.3,\n",
    "              15.1,15.3,15.0,15.6,15.7,14.8,14.5,14.2,14.9,14.9,\n",
    "              15.2,15.0,15.3,15.6,15.1,14.9,14.2,14.6,15.8,15.2,\n",
    "              15.9,15.2,15.0,14.9,14.8,14.5,15.1,15.5,15.5,15.1,\n",
    "              15.1,15.0,15.3,14.7,14.5,15.5,15.0,14.7,14.6,14.2])\n",
    "stat_val, p_val = ss.kstest(a, 'norm', [a.mean(), a.std(ddof=1)])\n",
    "print(stat_val, p_val)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "H<sub>0</sub>: ball diameters conform to the normal distribution. p-value > 0.05, so accpet H<sub>0</sub>\n",
    "\n",
    "___"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Homework\n",
    "\n",
    "1. Using curve_ Fit fits the Gaussian distribution with a Gaussian distribution function of \n",
    "$y=a\\cdot exp(-\\frac{(x-b)^2}{(2c^2)}),x \\in [0,10]$\n",
    ", where the true values$ a=1, b=5, c=2$. Try to fit $y$ with noise and compare it with real data by plotting\n",
    "\n",
    "2. Generate 1000 random numbers using a gamma distribution with parameter 1, draw histograms of these samples, and plot a PDF (probability density function) of this gamma distribution on them.\n",
    "\n",
    "3. Using Python for hypothesis testing analysis\n",
    "\n",
    "Gender: 1 being male and 2 being female;Data used: homework8.3.csv\n",
    "\n",
    "List of issues:\n",
    "\n",
    "(1). Is the overall average human body temperature 98.6 degrees Fahrenheit?\n",
    "\n",
    "(2). Does the temperature of the human body follow a normal distribution? Draw a histogram of the distribution.\n",
    "\n",
    "(3). What are the abnormal data in human questioning?\n",
    "\n",
    "(4). Is there any abnormality in the body temperature of men and women?\n",
    "\n",
    "(5). Is there a correlation between body temperature and heart rate?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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